Multi-fidelity data fusion prediction method fusing neighborhood information and fidelity perception attention

Abstract

This invention proposes a multi-fidelity data fusion prediction method that integrates neighborhood information and fidelity-aware attention. First, based on the specific application scenario, a cross-fidelity sample dataset covering the entire design space is constructed, and dimensional and distribution differences are eliminated through standardization. Second, a prediction model is trained using this cross-fidelity sample dataset. This prediction model consists of an adaptive neighborhood construction module and a fidelity-aware multi-head attention fusion module connected in series. Finally, newly acquired low-fidelity data is input into the trained prediction model to obtain the prediction result. This invention accurately captures local features through anchor-driven adaptive neighborhood construction, achieves differentiated information fusion through a fidelity-aware multi-head attention mechanism, and balances fitting accuracy and generalization ability through a joint loss optimization strategy. This enables high-precision fusion modeling of sparse high-fidelity data and redundant low-fidelity data in high-dimensional nonlinear scenarios, meeting the requirements of engineering prediction accuracy and model robustness.

Description

Technical Field

[0001] This invention relates to the field of data fusion technology, specifically to a multi-fidelity data fusion prediction method that integrates neighborhood information and fidelity-aware attention. Background Technology

[0002] In modern scientific computing and engineering design, the increasing demands for model complexity and accuracy have made balancing computational efficiency and prediction accuracy a core challenge. Multi-Fidelity Modeling (MFM) leverages the strengths of both low-fidelity (LF) and high-fidelity (HF) data to address this challenge. LF data, derived from simplified physical models or low-cost numerical computations, offers broad coverage and rapid generation, but its simplification of physical assumptions limits prediction accuracy. HF data, on the other hand, originates from high-precision numerical simulations or physical experiments, accurately reflecting complex physical details, but is extremely expensive to acquire and typically has sparse sample sizes.

[0003] Existing multi-fidelity data fusion methods have significant limitations when dealing with high-dimensional nonlinear engineering scenarios such as airfoil aerodynamic characteristic prediction and aircraft flow field simulation, specifically in the following aspects:

[0004] 1. Traditional Co-Kriging Methods: Methods such as those proposed by Dong et al. (2015) rely on the covariance structure of Gaussian processes to correlate data across fidelity, achieving stable predictions in low-dimensional scenarios. However, when facing high-dimensional nonlinear problems (e.g., dimension d≥10), the computational complexity of its covariance matrix increases exponentially with the sample size (O(N³), and it struggles to handle non-uniform data distributions and discontinuous physical quantities (e.g., shock discontinuities in transonic flow fields), leading to significant prediction biases and failing to meet engineering accuracy requirements.

[0005] Multifidelity modeling methods based on neural networks include multifidelity neural networks (MFNN, Meng et al., 2020) and multifidelity data aggregation convolutional neural networks (MDACNN, Chen et al., 2022). The former models cross-fidelity relationships by separating linear and nonlinear correlation terms, but it is difficult to capture local fine features when HF samples are sparse and unevenly distributed. The latter, although it introduces convolution operations to associate high-fidelity and low-fidelity data, fails to effectively distinguish the systematic biases between the two, and blind fusion is prone to introducing LF redundant noise, reducing the robustness of the model.

[0006] Existing attention enhancement methods, such as the LSTM-attention model proposed by Zhou et al. (2024), attempt to improve fusion performance by allocating data weights through attention mechanisms. However, these methods mostly employ global attention mechanisms, failing to balance local structural features with global trend consistency. In complex scenarios such as high gradient regions, phase shifts, or high-frequency oscillations, their generalization ability remains insufficient, making it difficult to effectively capture the local details of HF samples.

[0007] In summary, existing multi-fidelity data fusion technologies still suffer from three major shortcomings: insufficient HF sparse local modeling, significant LF redundancy interference, and lack of adaptive fusion strategies. There is an urgent need for a multi-fidelity data fusion method that can effectively integrate neighborhood information and fidelity perception mechanisms to improve the modeling accuracy and generalization ability in high-dimensional nonlinear engineering scenarios. Summary of the Invention

[0008] To address the shortcomings of existing multi-fidelity data fusion techniques in handling high-dimensional nonlinear engineering scenarios such as airfoil aerodynamic characteristic prediction and aircraft flow field simulation—including insufficient HF sparse local modeling, significant LF redundancy interference, and a lack of adaptive fusion strategies—leading to insufficient prediction accuracy and low model robustness—this invention proposes a multi-fidelity data fusion prediction method that integrates neighborhood information and fidelity-aware attention. This method accurately captures local features through anchor-driven adaptive neighborhood construction, achieves differentiated information fusion through a fidelity-aware multi-head attention mechanism, and balances fitting accuracy and generalization ability through a joint loss optimization strategy. This enables high-precision fusion modeling of sparse high-fidelity data and redundant low-fidelity data in high-dimensional nonlinear scenarios, meeting the requirements for engineering prediction accuracy and model robustness.

[0009] The technical solution of this invention is as follows:

[0010] A multi-fidelity data fusion prediction method that integrates neighborhood information and fidelity-aware attention includes the following steps:

[0011] Step 1: Based on the specific application scenario, construct a cross-fidelity sample dataset covering the entire design space, and eliminate the differences in units and distributions through standardization processing; the cross-fidelity sample dataset includes a high-fidelity (HF) sample set and a low-fidelity (LF) sample set, and each sample includes input features and corresponding sample output;

[0012] Step 2: Train a prediction model using the cross-fidelity sample dataset. The prediction model consists of an adaptive neighborhood construction module and a fidelity-aware multi-head attention fusion module connected in series.

[0013] In the adaptive neighborhood construction module, a structured neighborhood is constructed by taking each HF sample as an anchor point and combining the local gradient features of the LF data; the local neighborhood matrices of all HF samples are stacked according to the sample dimensions to form a three-dimensional tensor.

[0014] In the fidelity-aware multi-head attention fusion module, the three-dimensional tensor output by the adaptive neighborhood construction module is subjected to high-dimensional mapping and fidelity semantic injection. Then, the local fusion output of each attention head is obtained through HF-specific attention calculation. Finally, the local fusion output is subjected to feature fusion to obtain the final HF prediction vector.

[0015] During training, the loss function used is the joint loss function, which consists of the MSE prediction error term and... The regularization term is composed of the MSE prediction error term, which is calculated based on the sample output of the high-fidelity HF sample set as the label.

[0016] Step 3: Input the acquired new low-fidelity LF data into the trained prediction model to obtain the prediction results.

[0017] Further preferred solutions, specifically including in step 1:

[0018] Step 1.1: Collect dense LF sample sets and sparse HF sample sets to construct a cross-fidelity dataset; the LF sample set is denoted as... , For input features, For LF output, The number of samples in the LF sample set; the number of samples in the HF sample set. , For input features, For HF output, The number of samples in the HF sample set;

[0019] Step 1.2: Input features Perform normalization and map to The interval, the formula is:

[0020]

[0021] in To find the global minimum and maximum values ​​of the input features, avoid the impact of differences in the magnitude of inputs from different dimensions on model training; for the output... Standardization is performed, and the formula is:

[0022]

[0023] in The mean, The standard deviation is used to ensure consistency across the fidelity sample space through data alignment.

[0024] In a further preferred embodiment, step 2, the specific processing steps of the adaptive neighborhood construction module include:

[0025] Step 2.1: Average nearest neighbor distance using HF samples Initialize the basic step size :

[0026]

[0027] in Scaling factor, empirical range ;

[0028] Step 2.2: For HF anchor points Based on the input LF data at the HF anchor point Local gradient at Modulation step size :

[0029]

[0030] For the first The nearest neighbor distance of each HF anchor point;

[0031] Step 2.3: Anchor with HF Centered on, according to step size Generate symmetric neighborhoods:

[0032]

[0033] in For boundary constraint functions, Corresponding to the HF anchor point itself, For neighborhood expansion points;

[0034] Step 2.4: Anchor points Each neighboring point Construct the triplet feature vector:

[0035]

[0036] in For neighborhood points LF output, For fidelity indication;

[0037] Step 2.4: Concatenate all feature vectors in the neighborhood in spatial order to form anchor points. Local neighborhood matrix Stack the local neighborhood matrices of all HF samples according to the sample dimensions to form a three-dimensional tensor. .

[0038] A further preferred approach, in step 2.1, is to calculate the average nearest neighbor distance of the HF samples. for:

[0039] .

[0040] In a further optimized approach, the specific processing procedure of the fidelity-perceived multi-head attention fusion module in step 2 is as follows:

[0041] Step 2.5: Process the input 3D tensor Perform high-dimensional mapping and high-fidelity semantic injection:

[0042] For training tensors The first in The HF anchor point of the first Neighboring points Embedded representation is:

[0043]

[0044] in For neighborhood points The eigenvectors of the triplet, For the projection matrix, For neighborhood points Fidelity label These are learnable HF semantic vectors;

[0045] Step 2.6: For the three-dimensional tensor Each HF anchor point in the process is assigned a dedicated attention head, where the first... Local fusion output of attention heads at each HF anchor point :

[0046]

[0047] Among the queries ,key ,value , To train tensors The Middle The embedded neighborhood feature matrix corresponding to each HF anchor point These are the learnable weight matrices; For dimensional scaling factor, These are the weighting coefficients;

[0048] Step 2.7: Local fusion output Context vector generation, residual connection and layer normalization, and nonlinear transformation operations are performed sequentially to obtain the predicted value of a single HF anchor point:

[0049]

[0050] in , The predicted values ​​of all HF anchor points are concatenated in spatial order to form the final HF prediction vector. .

[0051] In a further optimized approach, in step 2, the joint loss function is:

[0052]

[0053] in This is the MSE prediction error term. for Regularization term, The regularization coefficient is used.

[0054]

[0055]

[0056] in It is the set of all trainable parameters in the prediction model.

[0057] A further preferred option, in step 2.3, is when or When using mirror filling, ensure the continuity of gradients at the boundaries.

[0058] A further preferred embodiment is that the application scenario is airfoil aerodynamic characteristic prediction, the input feature is the chord length ratio of the airfoil surface coordinates, and the prediction output is the pressure coefficient at the corresponding position on the airfoil surface.

[0059] Beneficial effects

[0060] Compared with the prior art, the present invention has the following beneficial effects:

[0061] This invention targets high-dimensional nonlinear engineering scenarios such as airfoil aerodynamic characteristic prediction and aircraft flow field simulation. By establishing a cross-fidelity dataset and preprocessing and training an optimized prediction model that combines an adaptive neighborhood construction module and a fidelity-aware multi-head attention fusion module, the sparse HF data and redundant LF data in high-dimensional nonlinear scenarios are processed into high-precision and highly generalizable fusion prediction results.

[0062] First, this invention utilizes anchor-driven adaptive neighborhood construction, centering on high-fidelity samples and dynamically adjusting the sampling density based on the local gradients of low-fidelity data. This achieves dense sampling in high-gradient regions, effectively solving the problem of local feature loss caused by the sparsity of high-fidelity samples. In RAE2822 airfoil shock region prediction, the agreement with high-fidelity data is improved by more than 15%.

[0063] Secondly, this invention introduces explicit fidelity semantic embedding and a high-fidelity dedicated attention head through a fidelity-aware multi-head attention module, prioritizing high-confidence, high-fidelity features and suppressing low-fidelity redundant noise.

[0064] Third, this invention, through a joint loss optimization strategy, balances the fitting accuracy of high-fidelity samples with the model's generalization ability, ensuring that the method has stable performance in both high-dimensional nonlinear numerical functions and engineering scenarios.

[0065] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0066] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which:

[0067] Figure 1 This is a model block diagram of the multi-fidelity data fusion prediction method that integrates neighborhood information and fidelity-aware attention, provided in the embodiments of the present invention.

[0068] Figure 2 This is a comparison chart of Forrester function (linear correlation) predictions provided in an embodiment of the present invention;

[0069] Figure 3 This is a comparison chart of predictions for continuous oscillation nonlinear functions provided in an embodiment of the present invention;

[0070] Figure 4 This is a comparison chart of phase offset oscillation function predictions provided in the embodiments of the present invention;

[0071] Figure 5 This is a schematic diagram of the RAE2822 airfoil structure provided in an embodiment of the present invention;

[0072] Figure 6 This is a comparison chart of the original HF (wind tunnel) and LF (CFD) data of RAE2822 provided in this embodiment of the invention;

[0073] Figure 7 This is a comparison chart of the predicted pressure coefficient of the RAE2822 airfoil provided in an embodiment of the present invention. Detailed Implementation

[0074] Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0075] This embodiment takes the transonic pressure coefficient prediction application scenario of the RAE2822 airfoil as an example. This embodiment corresponds to a core scenario in aircraft aerodynamic design, and the operating condition is: Mach number Angle of attack Reynolds number The target for prediction is the pressure coefficient along the entire chord of the airfoil. .

[0076] Specifically, the following steps are included:

[0077] Step 1: Construct a cross-fidelity sample dataset covering the entire design space, and eliminate differences in dimensions and distributions through standardization. The cross-fidelity sample dataset includes a high-fidelity (HF) sample set and a low-fidelity (LF) sample set, and each sample includes input features and corresponding sample outputs.

[0078] Step 1.1: Collect dense LF sample sets and sparse HF sample sets to construct a cross-fidelity dataset; the LF sample set is denoted as... , For input features, For LF output, The number of samples in the LF sample set; the number of samples in the HF sample set. , For input features, For HF output, The number of samples in the HF sample set;

[0079] In this embodiment, the HF data is from the RAE2822 airfoil wind tunnel test, with a total of 20 measuring points, 10 on the upper and 10 on the lower surface. The input is the proportion of the coordinate chord of the airfoil surface. , For the airfoil surface coordinates, For the airfoil chord length, the range of values ​​is... The output is the pressure coefficient. The LF data consists of 100 CFD numerical simulation samples, covering the upper and lower surfaces of the airfoil. The input and output are consistent with HF.

[0080] Step 1.2: Input features Perform normalization and map to The interval, the formula is:

[0081]

[0082] in To find the global minimum and maximum values ​​of the input features, avoid the impact of differences in the magnitude of inputs from different dimensions on model training; for the output... Standardization is performed, and the formula is:

[0083]

[0084] in The mean, The standard deviation is used to ensure consistency across the fidelity sample space through data alignment.

[0085] In this embodiment, the input Already The interval does not require normalization for the output. Using the mean of LF data Standard deviation Standardization (formula) HF data synchronization standardization ensures consistent data distribution.

[0086] In this embodiment, the HF sample size across the fidelity dataset is 20, the LF sample size is 100, and the input dimension is... (only ), with an output dimension of 1 (only ).

[0087] Step 2: Train a prediction model using the cross-fidelity sample dataset. The prediction model consists of an adaptive neighborhood construction module and a fidelity-aware multi-head attention fusion module connected in series.

[0088] In the adaptive neighborhood construction module, a structured neighborhood is constructed using each HF sample as an anchor point and combined with the local gradient features of the LF data. The local neighborhood matrices of all HF samples are stacked according to the sample dimensions to form a three-dimensional tensor. Through adaptive neighborhood construction, a precise correlation between HF and LF data is achieved, solving the problem of sparse local modeling of HF data.

[0089] In this embodiment, the specific processing steps of the adaptive neighborhood construction module include:

[0090] Step 2.1: Average nearest neighbor distance using HF samples Initialize the basic step size :

[0091]

[0092] in Scaling factor, empirical range ;

[0093] In this embodiment:

[0094]

[0095] and take Then the global step size .

[0096] Step 2.2: For HF anchor points Based on the input LF data at the HF anchor point Local gradient at Modulation step size :

[0097]

[0098] For the first The nearest neighbor distance of HF anchor points is used to shrink the high gradient region to achieve dense sampling, while the low gradient region is enlarged to avoid redundant sampling.

[0099] In this embodiment, 20 HF samples are used as anchor points, and local linear interpolation estimation of LF data is performed. gradient For example, when (Suction peak area) Adaptive step size ; and when (Tail edge area) , .

[0100] Step 2.3: Anchor with HF Centered on, according to step size Generate symmetric neighborhoods:

[0101]

[0102] in For boundary constraint functions, ensure that nodes are within... Inside, Corresponding to the HF anchor point itself, As a neighborhood expansion point, in this embodiment, the total number of neighborhood nodes is... The preferred value is 5, that is Covering 5 key sampling points:

[0103]

[0104] This balances local representativeness with computational efficiency, avoiding an excessive number of nodes that could cause a surge in tensor dimensions.

[0105] In RAE2822 airfoil prediction, if the number of nodes is 3 ( ), high gradient region (such as suction peak) The sampling density is insufficient to capture... The mutation characteristics indicate a prediction bias exceeding 10%; if the number of nodes is 7 ( While it can improve local accuracy, the training tensor dimension decreases from... Increase to The computational cost increases by 40%, especially in low gradient regions (such as the trailing edge). Introducing redundant nodes increases the risk of model overfitting, thus balancing local detail capture with computational efficiency.

[0106] Furthermore, for the neighborhood boundary filling strategy, "mirror filling" is used instead of traditional "constant filling" when a neighboring node exceeds the input domain. At that time, that is or At that time, through ( Mirror nodes are generated for boundary values ​​of 0 or 1 to ensure gradient continuity at the boundary. In this embodiment, mirror nodes are generated at the leading edge of the RAE2822 airfoil. and trailing edge In the generation of the HF anchor neighborhood, when the node exceeds... interval (e.g.) hour, ), Mirror filling through ( Generate mirror nodes (e.g., 0 or 1) This ensures continuity at the boundary; however, using constant fill (such as 0 fill) can lead to problems in the leading edge region. The prediction shows a plateau-shaped bias, with an RMSE 18% higher than that of mirror fill. Mirror fill can keep the prediction accuracy of the boundary area consistent with that of the interior area.

[0107] Step 2.4: Anchor points Each neighboring point Construct a triplet feature vector containing "spatial location-LF trend-fidelity identifier":

[0108]

[0109] in For neighborhood points The LF output provides local trend information. To indicate the fidelity, HF samples are assigned a value of 1, and LF samples are assigned a value of 0, explicitly distinguishing the reliability of the data.

[0110] Step 2.4: Concatenate all feature vectors in the neighborhood in spatial order to form anchor points. Local neighborhood matrix Stack the local neighborhood matrices of all HF samples according to the sample dimensions to form a three-dimensional tensor. .

[0111] In the fidelity-aware multi-head attention fusion module, the three-dimensional tensor output by the adaptive neighborhood construction module is subjected to high-dimensional mapping and fidelity semantic injection. Then, the local fusion output of each attention head is obtained through HF-specific attention calculation. Finally, the local fusion output is subjected to feature fusion to obtain the final HF prediction vector.

[0112] A fidelity-aware multi-head attention fusion module is used to achieve differentiated information fusion dominated by HF anchors and assisted by LF neighborhoods, enhancing the model's focus on high-fidelity features. The specific processing procedure is as follows:

[0113] Step 2.5: Process the input 3D tensor Perform high-dimensional mapping and high-fidelity semantic injection:

[0114] For training tensors The first in The HF anchor point of the first Neighboring points Embedded representation is:

[0115]

[0116] in For neighborhood points The eigenvectors of the triplet, For the projection matrix, For neighborhood points Fidelity label The HF semantic vector is a learnable vector, and high-fidelity and low-fidelity semantic features are explicitly distinguished by fidelity identifiers.

[0117] In this embodiment, the hidden space dimension Linear projection matrix , The initial values ​​are 0 and 0.01, and a projection matrix is ​​used. By mapping 3D neighborhood features to a 64D latent space, learnable HF semantic vectors are introduced. , The initial values ​​are set to a vector of all 1s, and the vector is updated adaptively during training.

[0118] Step 2.6: For the three-dimensional tensor Each HF anchor point is assigned a dedicated attention head, responsible only for feature fusion in its corresponding neighborhood, avoiding cross-anchor point interference; a scaled dot product attention with weighted coefficients is used to balance the sharpness and robustness of the weight distribution, resulting in the... Local fusion output of attention heads at each HF anchor point :

[0119]

[0120] Among the queries ,key ,value , To train tensors The Middle The embedded neighborhood feature matrix corresponding to each HF anchor point These are the learnable weight matrices; Use the dimension scaling factor to avoid Too large an amount will cause the attention score to overflow. The weighting coefficients are used to avoid excessive weighting of the HF anchor point while ignoring useful LF neighborhood information. Generated by the HF central node, ensuring that HF ​​features dominate weight allocation. and It includes neighborhood auxiliary information.

[0121] In this embodiment, the coefficient 0.8 is preferred over 0.5 or 1.2. In the shock wave region of the RAE2822 airfoil ( In the fusion process, if P=0.5, the attention weight is overly concentrated on the HF anchor point (weight ratio >80%), ignoring the auxiliary clues of the neighborhood to the shock wave position trend, resulting in a shock wave position prediction offset of 0.02 chord lengths; if P=1.2, the weight distribution is too scattered (HF anchor point weight ratio <40%), introducing systematic biases in the LF data (such as CFD shock wave hysteresis); when P=0.8, the HF anchor point weight ratio is about 60%, which can accurately capture the shock wave position information of HF, while using the LF neighborhood to correct local fluctuations, and the RMSE of the shock wave region prediction is reduced by 22% compared with the case without temperature coefficient.

[0122] Step 2.7: Local fusion output Proceed in sequence:

[0123] Context vector generation: via Operation will Flattened into a 1-dimensional context vector ;

[0124] Residual Connectivity and Layer Normalization: Introducing Residual Connectivity Preserve original neighborhood features and avoid information loss caused by attention calculation;

[0125] Layer normalization (LayerNorm) can mitigate the internal covariate bias, as shown in the formula: ;

[0126] Nonlinear transformation: Through multilayer perceptron (MLP) and layer normalization, the predicted value of a single HF anchor point is obtained: LayerNorm is used to mitigate internal covariate offset;

[0127] The predicted values ​​of all HF anchor points are concatenated in spatial order to form the final HF prediction vector. .

[0128] In this embodiment, a 128-neuron hidden layer MLP structure is used. The MLP is specifically configured with an input dimension of 64 (…). ) + 128-neuron hidden layer (ReLU activation) + output dimension 1 (Linear activation), instead of 64 or 256 neurons: 64-neuron hidden layers lead to underfitting of features, at the wing-shaped suction peak of The predicted amplitude deviation exceeds 8%; 256 hidden layers will double the number of model parameters and extend the training time to 1.8 times the original time; 128 hidden layers can meet the real-time requirements of engineering.

[0129] During training, the loss function used is the joint loss function, which consists of the MSE prediction error term and... Composition of regularization terms;

[0130]

[0131] in This is the MSE prediction error term. for Regularization term, The regularization coefficient has a range of values. ;

[0132]

[0133]

[0134] in It is the set of all trainable parameters in the prediction model.

[0135] In this embodiment, the regularization coefficient of the joint loss function In the RAE2822 airfoil model training, if The model exhibits significant overfitting to HF samples, with excessive suppression of parameter updates leading to underfitting. At this point, the optimal balance between fitting accuracy and generalization ability is achieved.

[0136] During training, the Adam optimizer was used with an initial learning rate of 1e-3 and a weight decay of 1e-5. Training was conducted for 2000 epochs, and an EarlyStoppin mechanism was introduced to calculate the error between the prediction result and the HF label. Satisfying the preset threshold ( This was determined to be the optimal prediction model.

[0137] Step 3: Input the acquired new low-fidelity LF data into the trained prediction model to obtain the prediction results.

[0138] In this embodiment, stratified sampling is used to select test samples instead of random sampling. In the RAE2822 airfoil test set, samples are selected according to... The interval is divided into "leading edge region" Suction peak region Shock zone Tail edge region "Four strata, with one HF sample and 25 LF samples extracted from each stratum to ensure that the test set covers all key aerodynamic regions of the airfoil; if random sampling is used, the test set may be missing shock wave region samples, which may lead to misjudgment of accuracy."

[0139] Figures 2 to 4 The figures show a comparison of the predictions made by this invention on the Forrester function (linear correlation), the continuous oscillation nonlinear function, and the phase-shifted oscillation function. Figure 7 The image shows a comparison of the predicted pressure coefficient for the RAE2822 airfoil. As can be seen from the image, the method described in this invention outperforms existing methods such as MFNN and MDACNN in terms of local feature capture, global trend consistency, and resistance to noise interference.

[0140] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention without departing from the principles and spirit of the present invention.

Claims

1. A multi-fidelity data fusion prediction method that integrates neighborhood information and fidelity-aware attention, characterized in that: Includes the following steps: Step 1: Based on the specific application scenario, construct a cross-fidelity sample dataset covering the entire design space, and eliminate the differences in units and distributions through standardization processing; the cross-fidelity sample dataset includes a high-fidelity (HF) sample set and a low-fidelity (LF) sample set, and each sample includes input features and corresponding sample output; Step 2: Train a prediction model using the cross-fidelity sample dataset. The prediction model consists of an adaptive neighborhood construction module and a fidelity-aware multi-head attention fusion module connected in series. In the adaptive neighborhood construction module, a structured neighborhood is constructed by taking each HF sample as an anchor point and combining the local gradient features of the LF data; the local neighborhood matrices of all HF samples are stacked according to the sample dimensions to form a three-dimensional tensor. In the fidelity-aware multi-head attention fusion module, the three-dimensional tensor output by the adaptive neighborhood construction module is subjected to high-dimensional mapping and fidelity semantic injection. Then, the local fusion output of each attention head is obtained through HF-specific attention calculation. Finally, the local fusion output is subjected to feature fusion to obtain the final HF prediction vector. During training, the loss function used is the joint loss function, which consists of the MSE prediction error term and... The regularization term consists of the MSE prediction error term, which is calculated based on the sample output of the high-fidelity HF sample set as the label. Step 3: Input the acquired new low-fidelity LF data into the trained prediction model to obtain the prediction results.

2. The multi-fidelity data fusion prediction method according to claim 1, which integrates neighborhood information and fidelity-aware attention, is characterized in that: Step 1 specifically includes: Step 1.1: Collect dense LF sample sets and sparse HF sample sets to construct a cross-fidelity dataset; the LF sample set is denoted as... , For input features, For LF output, The number of samples in the LF sample set; the number of samples in the HF sample set. , For input features, For HF output, The number of samples in the HF sample set; Step 1.2: Input features Perform normalization and map to The interval, the formula is: in To find the global minimum and maximum values ​​of the input features, avoid the impact of differences in the magnitude of inputs from different dimensions on model training; for the output... Standardization is performed, and the formula is: in The mean, The standard deviation is used to ensure consistency across the fidelity sample space through data alignment.

3. The multi-fidelity data fusion prediction method according to claim 1, which integrates neighborhood information and fidelity-aware attention, is characterized in that: In step 2, the specific processing steps of the adaptive neighborhood construction module include: Step 2.1: Average nearest neighbor distance using HF samples Initialize the basic step size : in Scaling factor, empirical range ; Step 2.2: For HF anchor points Based on the input LF data at the HF anchor point Local gradient at Modulation step size : For the first The nearest neighbor distance of each HF anchor point; Step 2.3: Anchor with HF Centered on, according to step size Generate symmetric neighborhoods: in For boundary constraint functions, Corresponding to the HF anchor point itself, For neighborhood expansion points; Step 2.4: Anchor points Each neighboring point Construct the triplet feature vector: in For neighborhood points LF output, For fidelity indication; Step 2.4: Concatenate all feature vectors in the neighborhood in spatial order to form anchor points. Local neighborhood matrix Stack the local neighborhood matrices of all HF samples according to the sample dimensions to form a three-dimensional tensor. .

4. The multi-fidelity data fusion prediction method according to claim 3, which integrates neighborhood information and fidelity-aware attention, is characterized in that: In step 2.1, the average nearest neighbor distance of HF samples... for: 。 5. The multi-fidelity data fusion prediction method according to claim 3, which integrates neighborhood information and fidelity-aware attention, is characterized in that: In step 2, the specific processing procedure of the fidelity-aware multi-head attention fusion module is as follows: Step 2.5: Process the input 3D tensor Perform high-dimensional mapping and high-fidelity semantic injection: For training tensors The first in The first HF anchor point neighborhood points Embedded representation is: in For neighborhood points The eigenvectors of the triplet, Let be the projection matrix. For neighborhood points Fidelity label These are learnable HF semantic vectors; Step 2.6: For the three-dimensional tensor Each HF anchor point in the process is assigned a dedicated attention head, where the first... Local fusion output of attention heads at individual HF anchor points : Among the queries ,key ,value , To train tensors The Middle The embedded neighborhood feature matrix corresponding to each HF anchor point These are the learnable weight matrices; For dimensional scaling factor, These are the weighting coefficients; Step 2.7: Local fusion output Context vector generation, residual connection and layer normalization, and nonlinear transformation operations are performed sequentially to obtain the predicted value of a single HF anchor point: in , The predicted values ​​of all HF anchor points are concatenated in spatial order to form the final HF prediction vector. .

6. The multi-fidelity data fusion prediction method according to claim 1, characterized in that: In step 2, the joint loss function is: in This is the MSE prediction error term. for Regularization term, The regularization coefficient is used. in It is the set of all trainable parameters in the prediction model.

7. The multi-fidelity data fusion prediction method according to claim 3, which integrates neighborhood information and fidelity-aware attention, is characterized in that: In step 2.3, when or When using mirror filling, ensure the continuity of gradients at the boundaries.

8. The multi-fidelity data fusion prediction method according to claim 1, characterized in that: The application scenario is airfoil aerodynamic characteristic prediction. The input feature is the chord length ratio of the airfoil surface coordinates, and the prediction output is the pressure coefficient at the corresponding position on the airfoil surface.

Images